The problem of the morphological stability of an interface in the case of the displacement of one non-Newtonian fluid by another non-Newtonian fluid in a radial Hele-Shaw cell has been considered. Both fluids have been described by the two-parameter Ostwald–de Waele power-law model. The nonzero viscosity of the displacing fluid has been taken into account. A generalized Darcy's law for the system under consideration, as well as an equation for the determination of the critical size of morphological stability with respect to harmonic perturbations (linear analysis), has been derived. Morphological phase diagrams have been constructed, and the region of the parameters in which nonequilibrium reentrant morphological transitions are possible has been revealed.

We present an alternative perspective on nonharmonic mode coexistence, commonly found in the shear layer spectrum of open-cavity flows. Modes obtained by a local linear stability analysis of perturbations to a two-dimensional, incompressible, and inviscid sheared flow over a cavity of finite length and depth were conditioned by a so-called coincidence condition first proposed by Kulikowskii [J. Appl. Math. Mech. 30, 180 (1966)] which takes into account instability wave reflection within the cavity. The analysis yields a set of discrete, nonharmonic frequencies, which compare well with experimental results [Phys. Fluids 20, 114101 (2008); Exp. Fluids 50, 905 (2010)].

The mechanical and transport properties of a Bentheim sandstone are studied both experimentally and numerically. Three classical classes of loads are applied to a sample whose permeability is measured. The elasticity and the Stokes equations are discretized on unstructured tetrahedral meshes which precisely follow the deformations of the sample. Numerical results are presented, discussed, and compared to the available experimental data.

Granular materials often segregate under mechanical agitation such as flowing, shaking, or rotating, in contrast to an expectation of mixing. It is well known that bidisperse mixtures of granular materials in a partially filled rotating cylinder exhibit monotonic coarsening dynamics of segregation. Here we report the steady oscillation of segregated axial bands under the stationary rotation of a nearly filled coaxial cylinder for $O\left({10}^3\right)$ revolutions. The axial bands demonstrate steady back-and-forth motion along the axis of rotation. Experimental findings indicated that these axial band dynamics are driven by global convection throughout the system. The essential features of the spatiotemporal dynamics are reproduced with a simple phenomenological equation that incorporates the effect of global convection.

The effect of defects on the percolation of linear $k$-mers (particles occupying $k$ adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The $k$-mers are deposited using a random sequential adsorption mechanism. Two models $L_d$ and $K_d$ are analyzed. In the $L_d$ model it is assumed that the initial square lattice is nonideal and some fraction of sites $d$ is occupied by nonconducting point defects (impurities). In the $K_d$ model the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the $k$-mers $d$ consists of defects, i.e., is nonconducting. The length of the $k$-mers $k$ varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependences of the percolation threshold concentration of the conducting sites $p_c$ vs the concentration of defects $d$ are analyzed for different values of $k$. Above some critical concentration of defects $d_m$, percolation is blocked in both models, even at the jamming concentration of $k$-mers. For long $k$-mers, the values of $d_m$ are well fitted by the functions $d_m\propto k_m^{-\alpha }-k^{-\alpha }$ ($\alpha =1.28\pm 0.01$ and $k_m=5900\pm 500$) and $d_m\propto {log}_{10}(k_m/k)$ ($k_m=4700\pm 1000$) for the $L_d$ and $K_d$ models, respectively. Thus, our estimation indicates that the percolation of $k$-mers on a square lattice is impossible even for a lattice without any defects if $k⪆6\times {10}^3$.

The Green-Kubo formula provides a mathematical expression for heat conductivity in terms of integrals of the heat-current correlation function, which should be calculated in the thermodynamic limit. In finite systems this function generally decreases, i.e., it decays faster than it does in infinite systems. We compared the values of the correlation function in a one-dimensional purely quartic lattice with various lengths, and found that this loss is much smaller than is conventionally estimated. By studying the heat diffusion process in this lattice, we found that, in contrast to the conventional belief, the collisions between sound modes do not noticeably affect the current correlation function. Therefore, its loss being surprisingly small can be well understood. This finding allows one to calculate the heat conductivity in a very large system with desirable accuracy by performing simulations in a system with much smaller size, and thus greatly broadens the application of the Green-Kubo method.

An explicit expression of the Stokes-Einstein (SE) relation in molecular scale has been determined for pure Lennard-Jones (LJ) liquids on the saturated vapor line using a molecular dynamics calculation with the Green-Kubo formula, as $D{\eta }_{\mathrm{sv}}=kT{\xi }^{-1}{(N/V)}^{1/3}$, where $D$ is the self-diffusion coefficient, ${\eta }_{\mathrm{sv}}$ the shear viscosity, $k$ the Boltzmann constant, $T$ the temperature, $\xi$ the constant, and $N$ the particle number included in the system volume $V$. To this end, the dependence of $D$ and ${\eta }_{\mathrm{sv}}$ on packing fraction, $\eta$, and $T$ has been determined so as to complete their scaling equations. The equations for $D$ and ${\eta }_{\mathrm{sv}}$ in these states are $m^{-1/2}{(N/V)}^{-1/3}{\left(1-\eta \right)}^4{\epsilon }^{-1/2}T$ and $m^{1/2}{(N/V)}^{2/3}{\left(1-\eta \right)}^{-4}{\epsilon }^{1/2}{T}^0$, respectively, where $m$ and $\epsilon$ are the atomic mass and characteristic parameter of energy used in the LJ potentials, respectively. The equations can well describe the behaviors of $D$ and ${\eta }_{\mathrm{sv}}$ for both the LJ and the real rare-gas liquids. The obtained SE relation justifies the theoretical equation proposed by Eyring and Ree, although the value of $\xi$ is slightly different from that given by them. The difference of the obtained expression from the original SE relation, $D{\eta }_{\mathrm{sv}}=(kT/2\pi ){\sigma }^{-1}$, where $\sigma$ means the particle size, is the presence of the ${\eta }^{1/3}$ term, since ${\left(N/V\right)}^{1/3}={\left(6/\pi \right)}^{1/3}{\sigma }^{-1}{\eta }^{1/3}$. Since the original SE relation is based on the fluid mechanics for continuum media, allowing the presence of voids in liquids is the origin of the ${\eta }^{1/3}$ term. Therefore, also from this viewpoint, the present expression is more justifiable in molecular scale than the original SE relation. As a result, the ${\eta }^{1/3}$ term cancels out the $\sigma$ dependence from the original SE relation. The present result clearly shows that it is not necessary to attribute the deviation from the original SE relation to any temperature dependence of particle size or to introduce the fractional SE relation for pure LJ liquids. It turned out that the $\eta$ dependence of both $D$ and ${\eta }_{\mathrm{sv}}$ is similar to that in the corresponding equations by the Enskog theory for hard sphere (HS) fluids, although the $T$ dependence is very different, which means that the difference in the behaviors of $D$ and ${\eta }_{\mathrm{sv}}$ between the LJ and HS fluids are traceable simply to their temperature dependence. Although the SE relation for the HS fluids also follows $D{\eta }_{\mathrm{sv}}=kT{\xi }^{-1}{(N/V)}^{1/3}$, the value of $\xi$ is significantly different from that for the LJ liquids.

We investigate the fragmentation process of solid materials with crystalline and amorphous phases using the the discrete element method. Damage initiates inside spherical samples above the contact zone in a region where the circumferential stress field is tensile. Cracks initiated in this region grow to form meridional planes. If the collision energy exceeds a critical value which depends on the material's internal structure, cracks reach the sample surface resulting in fragmentation. We show that this primary fragmentation mechanism is very robust with respect to the internal structure of the material. For all configurations, a sharp transition from the damage to the fragmentation regime is observed, with smaller critical collision energies for crystalline samples. The mass distribution of the fragments follows a power law for small fragments with an exponent that is characteristic for the branching merging process of unstable cracks. Moreover this exponent depends only on the dimensionally of the system and not on the microstructure.

We present a systematic Monte Carlo simulation study of thin nematic and cholesteric shells with planar anchoring using an off-lattice model. The results obtained using the simple model correspond with previously published results for lattice-based systems, with the number, type, and position of defects observed dependent on the shell thickness with four half-strength defects in a tetrahedral arrangement found in very thin shells and a pair of defects in a bipolar (boojum) configuration observed in thicker shells. A third intermediate defect configuration is occasionally observed for intermediate thickness shells, which is stabilized in noncentrosymmetric shells of nonuniform thickness. Chiral nematic (cholesteric) shells are investigated by including a chiral term in the potential. Decreasing the pitch of the chiral nematic leads to a twisted bipolar (chiral boojum) configuration with the director twist increasing from the inner to the outer surface.

We describe the emergence of the giant mutually connected component in networks of networks in which each node has a single replica node in any layer and can be interdependent only on its replica nodes in the interdependent layers. We prove that if, in these networks, all the nodes of one network (layer) are interdependent on the nodes of the same other interconnected layer, then, remarkably, the mutually connected component does not depend on the topology of the network of networks. This component coincides with the mutual component of the fully connected network of networks constructed from the same set of layers, i.e., a multiplex network.

We propose a discrete model of gas-free combustion of a cylindrical sample which reproduces in detail a spin combustion mode. It is shown that a spin combustion, in its classical sense as a continuous spiral motion of heat release zones on the surface of the sample, does not exist. Such a concept has arisen due to the misinterpretation of the experimental data. This study shows that in fact a spinlike combustion is realized, at which two energy release zones appear on the lateral surface of the sample and propagate circumferentially in the opposite directions. After some time two new heat release zones are formed on the next layer of the cylinder surface and make the same counter-circular motion. This process continues periodically and from a certain angle it looks like a spiral movement of the luminous zone along the lateral surface of the sample. The model shows that on approaching the combustion limit the process becomes more complicated and the spinlike combustion mode shifts to a more complex mode with multiple zones of heat release moving in different directions along the lateral surface. It is shown that the spin combustion mode appears due to asymmetry of initial conditions and always transforms into a layer-by-layer combustion mode with time.

Probe-tack measurements evaluate the adhesion strength of viscous fluids confined between parallel plates. This is done by recording the adhesion force that is required to lift the upper plate, while the lower plate is kept at rest. During the lifting process, it is known that the interface separating the confined fluids is deformed, causing the emergence of intricate interfacial fingering structures. Existing meticulous experiments and intensive numerical simulations indicate that fingering formation affects the lifting force, causing a decrease in intensity. In this work, we propose an analytical model that computes the lifting adhesion force by taking into account not only the effect of interfacial fingering, but also the action of wetting and viscous normal stresses. The role played by the system's spatial confinement is also considered. We show that the incorporation of all these physical ingredients is necessary to provide a better agreement between theoretical predictions and experiments.

An integrated simulation approach fully based on the particle-in-cell (PIC) model is proposed, which involves both fast-particle generation via laser solid-density plasma interaction and transport and energy deposition of the particles in extremely high-density plasma. It is realized by introducing two independent systems in a simulation, where the fast-particle generation is simulated by a full PIC system and the transport and energy deposition computed by a second PIC system with a reduced field solver. Data of the fast particles generated in the full PIC system are copied to the reduced PIC system in real time as the fast-particle source. Unlike a two-region approach, which takes a single PIC system and two field solvers in two plasma density regions, respectively, the present one need not match the field solvers since the reduced field solver and the full solver adopted respectively in the two systems are independent. A simulation case is presented, which demonstrates that this approach can be applied to integrated simulation of fast ignition with real target densities, e.g., 300 ${\mathrm{g/cm}}^3$.

A method for modeling realistic laser beams smoothed by kinoform phase plates is presented. The ray-based paraxial complex geometrical optics (PCGO) model with Gaussian thick rays allows one to create intensity variations, or pseudospeckles, that reproduce the beam envelope, contrast, and high-intensity statistics predicted by paraxial laser propagation codes. A steady-state cross-beam energy-transfer (CBET) model is implemented in a large-scale radiative hydrocode based on the PCGO model. It is used in conjunction with the realistic beam modeling technique to study the effects of CBET between coplanar laser beams on the target implosion. The pseudospeckle pattern imposed by PCGO produces modulations in the irradiation field and the shell implosion pressure. Cross-beam energy transfer between beams at ${20}^{\circ }$ and ${40}^{\circ }$ significantly degrades the irradiation symmetry by amplifying low-frequency modes and reducing the laser-capsule coupling efficiency, ultimately leading to large modulations of the shell areal density and lower convergence ratios. These results highlight the role of laser-plasma interaction and its influence on the implosion dynamics.

It is pointed out that the interaction of a magnet and a point charge has not been properly understood because the mutual interactions of the magnet's current carriers have been neglected. The magnet-point-charge interaction is important for understanding some theoretical paradoxes, such as the Shockley-James paradox, and for interpreting some experimentally observed effects, such as the Aharonov-Bohm and Aharonov-Casher phase shifts. Coleman and Van Vleck provide a discussion of the Shockley-James paradox where they note that internal relativistic mechanical momentum (hidden momentum) can be carried by the current carriers of the magnet. Although internal mechanical momentum is indeed dominant for noninteracting particles moving in a closed orbit under the influence of an external electric field, the presence of interactions among the magnet's current carriers leads to an internal electromagnetic momentum, which does not seem to be recognized in the physics literature. In the interacting multiparticle situation, the external charge induces an electrostatic polarization of the magnet, which leads to an internal electromagnetic momentum in the magnet where both the electric and magnetic fields for the momentum are contributed by the magnet particles. This internal electromagnetic momentum for the interacting multiparticle situation is equal in magnitude and opposite in direction compared to the familiar external electromagnetic momentum where the electric field is contributed by the external charged particle and the magnetic field is that due to the magnet. In the present article, the momentum balance of the Shockley-James situation for a system of a magnet and a point charge is calculated in detail for a magnet model consisting of two interacting point charges, which are constrained to move in a circular orbit on a frictionless ring with a compensating negative charge at the center.

In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential convergence is achieved rather than polynomial rates. The solution methodology proposed, the CCSLBM, is also extended to three dimensions and a 3D regularized cavity is simulated; the corresponding results are presented and validated. Indications are that the CCSLBM developed and applied herein is robust, efficient, and accurate for computing 2D and 3D low-speed flows. Note also that high-accuracy solutions obtained by applying the CCSLBM can be used as benchmark solutions for the assessment of other LBM-based flow solvers.

In this work, an interface-capturing lattice Boltzmann equation (LBE) model is proposed for two-phase flows. In the model, a Lax-Wendroff propagation scheme and a properly chosen equilibrium distribution function are employed. The Lax-Wendroff scheme is used to provide an adjustable Courant-Friedrichs-Lewy (CFL) number, and the equilibrium distribution is presented to remove the dependence of the relaxation time on the CFL number. As a result, the interface can be captured accurately by decreasing the CFL number. A theoretical expression is derived for the chemical potential gradient by solving the LBE directly for a two-phase system with a flat interface. The result shows that the gradient of the chemical potential is proportional to the square of the CFL number, which explains why the proposed model is able to capture the interface naturally with a small CFL number, and why large interface error exists in the standard LBE model. Numerical tests, including a one-dimensional flat interface problem, a two-dimensional circular droplet problem, and a three-dimensional spherical droplet problem, demonstrate that the proposed LBE model performs well and can capture a sharp interface with a suitable CFL number.

In the present research, we tried to improve the performance of the lattice Boltzmann (LB) -based adjoint approach by utilizing the mesoscopic inherent of the LB method. In this regard, two macroscopic discrete adjoint (MADA) and microscopic discrete adjoint (MIDA) approaches are used to answer the following two challenging questions. Is it possible to extend the concept of the macroscopic and microscopic variables of the flow field to the corresponding adjoint ones? Further, similar to the conservative laws in the LB method, is it possible to find the comparable conservation equations in the adjoint approach? If so, then a definite framework, similar to that used in the flow solution by the LB method, can be employed in the flow sensitivity analysis by the MIDA approach. This achievement can decrease the implementation cost and coding efforts of the MIDA method in complicated sensitivity analysis problems. First, the MADA and MIDA equations are extracted based on the LB method using the duality viewpoint. Meanwhile, using an elementary case, inverse design of a two-dimensional unsteady Poiseuille flow in a periodic channel with constant body forces, the procedure of analytical evaluation of the adjoint variables is described. The numerical results show that similar correlations between the distribution functions can be seen between the corresponding adjoint ones. Besides, the results are promising, emphasizing the flow field adjoint variables can be evaluated via the adjoint distribution functions. Finally, the adjoint conservative laws are introduced.

In this Rapid Communication, we study the behavior of a strongly diffusive passive scalar field $T$ submitted to a freely decaying, homogeneous and isotropic turbulence with eddy-damped quasinormal Markovian simulations. We present a new subrange located between the $k^{-17/3}$ inertial-diffusive subrange and the Kolmogorov wave number $k_{\eta }$. This subrange is generated by small-scale convection linked to $k_{\eta }$ that balances diffusion effects. Thus, we build a typical length scale $k_{CD}^{-1}$ based on convection and diffusion and give an expression for the shape of the passive scalar spectrum in this subrange $E_T\sim \sqrt{Pr}{k}^{-11/3}$ using physical arguments. This result unifies two different theories coming from Batchelor [G. K. Batchelor, J. Fluid. Mech. 5, 113 (1959)] and Chasnov [J. Chasnov et al., Phys. Fluids A 1, 1698 (1989)] and explains results previously obtained experimentally.

The Ziff-Gulari-Barshad (ZGB) model, a simplified description of the oxidation of carbon monoxide (CO) on a catalyst surface, is widely used to study properties of nonequilibrium phase transitions. In particular, it exhibits a nonequilibrium, discontinuous transition between a reactive and a CO poisoned phase. If one allows a nonzero rate of CO desorption $\left(k\right)$, the line of phase transitions terminates at a critical point $\left(k_c\right)$. In this work, instead of restricting the CO and atomic oxygen (O) to react to form carbon dioxide $\left({\mathrm{CO}}_2\right)$ only when they are adsorbed in close proximity, we consider a modified model that includes an adjustable probability for adsorbed CO and O atoms located far apart on the lattice to react. We employ large-scale Monte Carlo simulations for system sizes up to $240\times 240$ lattice sites, using the crossing of fourth-order cumulants to study the critical properties of this system. We find that the nonequilibrium critical point changes from the two-dimensional Ising universality class to the mean-field universality class upon introducing even a weak long-range reactivity mechanism. This conclusion is supported by measurements of cumulant fixed-point values, cluster percolation probabilities, correlation-length finite-size scaling properties, and the critical exponent ratio $\beta /\nu$. The observed behavior is consistent with that of the equilibrium Ising ferromagnet with additional weak long-range interactions [T. Nakada, P. A. Rikvold, T. Mori, M. Nishino, and S. Miyashita, Phys. Rev. B 84, 054433 (2011)]. The large system sizes and the use of fourth-order cumulants also enable determination with improved accuracy of the critical point of the original ZGB model with CO desorption.